We investigate the structure of the fixed-point algebra of ${\mathcal{O}}_n$ under the action of the cyclic permutation of the generating isometries. We prove that it is ⁎-isomorphic with ${\mathcal{O}}_n$, thus generalizing a result of Choi and Latrémolière on ${\mathcal{O}}_2$. As an application of the technique employed, we also describe the fixed-point algebra of ${\mathcal{O}}_{2n}$ under the exchange automorphism.

中文翻译：

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关于Cuntz代数及其不动点代数的循环自同构

我们研究了不动点代数的结构 ${\mathcal{哦}}_n$在生成等距的循环排列的作用下。我们证明它是⁎-同构的${\mathcal{哦}}_n$，从而将 Choi 和 Latrémolière 的结果推广到 ${\mathcal{哦}}_2$. 作为所采用技术的应用，我们还描述了${\mathcal{哦}}_{2n}$ 在交换自同构下。